Solve for $p$, $ -\dfrac{5p + 9}{3p^3} = \dfrac{6}{3p^3} - \dfrac{10}{6p^3} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $3p^3$ $3p^3$ and $6p^3$ The common denominator is $6p^3$ To get $6p^3$ in the denominator of the first term, multiply it by $\frac{2}{2}$ $ -\dfrac{5p + 9}{3p^3} \times \dfrac{2}{2} = -\dfrac{10p + 18}{6p^3} $ To get $6p^3$ in the denominator of the second term, multiply it by $\frac{2}{2}$ $ \dfrac{6}{3p^3} \times \dfrac{2}{2} = \dfrac{12}{6p^3} $ The denominator of the third term is already $6p^3$ , so we don't need to change it. This give us: $ -\dfrac{10p + 18}{6p^3} = \dfrac{12}{6p^3} - \dfrac{10}{6p^3} $ If we multiply both sides of the equation by $6p^3$ , we get: $ -10p - 18 = 12 - 10$ $ -10p - 18 = 2$ $ -10p = 20 $ $ p = -2$